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Sphericity of Cylinder

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Calculate the sphericity of a cylinder of dia 1 cm and height 3 cm.

Calculations:

\(\displaystyle \text{Sphericity} (\phi_s) = \frac{\text{surface area of sphere of same volume as the particle}}{\text{surface area of particle}} \)

Volume of particle = π r_{c}^{2} h = π x 0.5^{2} x 3 = 2.356 cm^{3}

Radius of sphere of volume 2.356 cm^{3}:

4πr_{s}^{3 }/ 3 = 2.356

r_{s} = 0.8255 cm

Surface area of sphere of same volume as the particle = 4 π r_{s}^{2} = 4 x πx 0.8255^{2} = 8.563 cm^{2}

Surface area of particle = 2 π r_{c} (h + r_{c}) = 2 x π x 0.5 x (3 + 0.5) = 10.996 cm^{2}

Sphericity (φ
_{s}) = 8.563/10.996 = 0.779

Sphericity could also be found from the formula,

Sphericity (φ
_{s}) = 6 V_{p} / (D_{p}S_{p})

Where V_{p} = volume of particle

D_{p} = Equivalent diameter of particle. (Equivalent diameter is defined as the diameter of a sphere of equal volume)

S_{p} = surface area of particle

V_{p} = π r_{c}^{2} h = 2.356 cm^{3}

D_{p} = 2 r_{s} = 2 x 0.8255 = 1.651 cm

S_{p} = 2 π r_{c} (h + r_{c}) = 10.996 cm^{2}

φ
_{s} = 6 x 2.356 / (1.651 x 10.996) = 0.779

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Last Modified on: 30-Apr-2024

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